Thermomechanical behavior of a plate composed of layers with different transparencies under the action of thermal radiat
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THERMOMECHANICAL BEHAVIOR OF A PLATE COMPOSED OF LAYERS WITH DIFFERENT TRANSPARENCIES UNDER THE ACTION OF THERMAL RADIATION R. F. Terlets’kyi and O. P. Turii
UDC 539.3
We study the thermal and mechanical processes running in a two-layer plate (in the case of perfect mechanical contact between the opaque and semitransparent layers) caused by the thermal radiation of a heated plane surface parallel to the composite plate and located on the side of the opaque layer. The contact boundary-value problem of heat conduction is reduced to an equivalent system of three nonlinear Volterra-type equations solved by the method of successive approximations. The dependences of the distributions of temperature and stresses in the plate on the ratio of thicknesses of the layers are investigated. It is shown that the influence of the thermal radiation of the opaque layer on the computed temperature in the plate is significant at temperatures higher than 530°K. As the thickness of the semitransparent layer decreases for a fixed thickness of the opaque layer, the temperature gradient across the thickness of the semitransparent layer sharply increases. The maximum tensile stresses in the plate may appear in the opaque or semitransparent layer depending on the ratio of the their thicknesses. For certain thicknesses of the semitransparent layer, they can attain the maximum permissible values.
In order to use the rational modes of operation [1, 2] or thermal processing [3, 4] of layered products with layers of different transparencies (partially transparent or opaque), it is necessary to estimate the temperatures and stresses induced in these products by thermal beams. In the literature, one can find various versions of the thermomechanics of homogeneous partially transparent bodies [5, 6] and bodies with admixtures [7, 8] subjected to the action of thermal radiation. The processes of propagation of thermal beams and heat conduction in layered semitransparent bodies are studied with the help of model problems for layered plates in [9–12]. The thermal stressed state of a layered partially irradiated transparent plate is investigated in [13], and the thermal stressed state of a bimetallic plate subjected to induction heating is analyzed in [14]. In what follows, we study the thermal stressed state of a plate formed by the opaque and semitransparent layers subjected to the action of thermal radiation from a heated surface located parallel to the composite plate on the side of the opaque layer. In formulating the boundary and contact conditions, we take into account the radiation heat transfer from the surfaces of the opaque layer. Statement of the Problem and the Procedure of Its Solution Consider a layered plate formed by the opaque and semitransparent layers with thicknesses h1 and h2 , respectively. The surface z = 0 of the plate (the z-axis is directed along the normal to the layers, z = h 1 is the interface of the layers, and z = h 1 + h2 = h is the opposite surface of the plate) is subjected to the action of thermal radiation from a
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